**5. Discussion**

In spring, summer, and autumn, heat energy was transferred into Ningwu ice cave through air and wall rock by thermal conduction, resulting in increasing the air temperature of the ice cave limitedly, because the efficiency of conduction is relatively low. But in winter, the air temperature of the ice cave decreases promptly, caused by air natural thermal convection. The water-ice phase change buffers the energy exchange. Considering these physical mechanisms, the modeling results present that (1) starting from a normal ground temperature distribution, a year-round ice deposit will be produced in the cave within a decade, about 5 years (**Figure 6a**), and the air temperature of the cave will drop gradually for more than a century, and also that (2) the air temperature of the ice cave will finally reach a quasi-stable cyclic state and will vary within a certain range (less than 1.0°C, from −3.9 to −2.9°C). At this stage, the annual total heat energy conducted into the cave and the heat energy removed from the cave by air natural convection are balanced.

Installing an airtight door at a cave entrance is what the Wudalianchi National Geological Park has done to "prevent" the ice deposit from melting every night during the tourist season and the entire winter. When the cave airtight door is closed, in fact, the air convection in winter is blocked. Consequently, cold air cannot enter the cave and cannot remove heat energy from the cave. Accumulation of heat energy conducted by air and rock will eventually cause the ice deposit to melt in Wudalianchi cave. Our modeling results present that it takes less than 40 years to completely melt the whole ice deposit in the cave. This means that Ningwu ice cave is probably not undergoing melting of the ice deposit at present. This study

also suggests that scientific management is significant for sustainable application of natural resources. Otherwise, well-meaning acts such as installing a door to completely seal the entrance will actually destroy the ice cave in a few decades.

We expect that no airtight door will be fixed at Zibaishan ice cave entrance and few people enter the ice cave before comprehensive and detailed studies, avoiding affecting its natural conditions.
